This paper generalizes the sequential estimation of autoregressive parameters as given in Gaver and Lewis (1980) of pth order processes EAR(p) and GAR(p). The first two moments of the stopping time distribution are computed for the EAR(2) process, a procedure for estimating the paramter lambda is given, and a simulation is given to show how large the stopping time can be for various alpha 1 and alpha 2.

Topics: DTIC Archive, Chernick,M R, AEROSPACE CORP EL SEGUNDO CA GUIDANCE AND CONTROL DIV, *ESTIMATES,...

The problem of hypothesis testing when the distribution is specified only up to a nuisance parameter is considered. A test is said to be adaptive if it is asymptotically optimal regardless of the value of the nuisance parameter. The exponential rate of convergence to zero of the probability of type II error when the probability of type I error converges to zero exponentially fast at a fixed rate is used as the optimal criterion. A necessary and sufficient condition for the existence of adaptive...

Topics: DTIC Archive, Mak, K S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *HYPOTHESES, *STATISTICAL...

If the number of factors in an experiment is increased, does it necessarily follow that the size of the experiment must increase to achieve a satisfactory analysis? In some common situations the answer is No. The present paper discusses a model suggested by medical diagnostic problems in which the answer is Yes: indeed, the increase in size is exponentially fast. The conclusion is drawn that statisticians should be cautions before embarking on the study of data with large numbers of factors...

Topics: DTIC Archive, Lindley,D V, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *PARAMETRIC...

A rational function is presented for approximating the function f(z) = coth z - 1/z that appears in several exponentially fitted or weighted finite difference and finite element methods for convection-diffusion problems. The approximation is less expensive to evaluate than f(z) and provides greater accuracy than the doubly asymptotic approximation when z = 0(1).

Topics: DTIC Archive, Flaherty, Joseph E, AIR FORCE OCCUPATIONAL MEASUREMENT CENTER RANDOLPH AFB TX,...

A new time series model for exponential variables having first order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (EAR(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of time nonreversibility effects in sample path behavior. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and...

Topics: DTIC Archive, Lawrance,A J, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *TIME SERIES ANALYSIS,...

A new time series model for exponential variables having first order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (EAR(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of time nonreversibility effects in sample path behavior. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and...

Topics: DTIC Archive, Lawrance,A J, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *TIME SERIES ANALYSIS,...

The Nakagami-m distribution is often suggested as the probability distribution appropriate for scintillation data. This report considers the statistical questions related to judging the goodness-of-fit of data to the Nakagami-m distribution. Both graphical and numerical techniques are discussed. (Author)

Topics: DTIC Archive, Tsipouras,P, BEDFORD RESEARCH ASSOCIATES MA, *PROBABILITY DISTRIBUTION FUNCTIONS,...

The Nakagami-m distribution is often suggested as the probability distribution appropriate for scintillation data. This report considers the statistical questions related to judging the goodness-of-fit of data to the Nakagami-m distribution. Both graphical and numerical techniques are discussed. (Author)

Topics: DTIC Archive, Tsipouras,P, BEDFORD RESEARCH ASSOCIATES MA, *PROBABILITY DISTRIBUTION FUNCTIONS,...

The problem we study in this paper is the estimation of the distribution function F under the assumption that F belongs to the class of NBU distributions. Without the NBU restriction, the empirical distribution function F(n) converges to F in several senses and at the best possible rate. However, F(n) need not to be NBU, and, in fact, it is not difficult to show that P(f(n) is NBU) going to 0 when sampling from some NBU distributions (for example, the exponential distribution). Our goal here is...

Topics: DTIC Archive, Samaniego,Francisco J, CALIFORNIA UNIV DAVIS INTERCOLLEGE DIV OF STATISTICS,...

Decreasing failure rates for electronic equipment used on the Polaris, Posiedon and Trident missile systems have been observed. The mixed exponential distribution has been shown to fit the life data for the electronic equipment on these systems. This paper discusses some of the estimation problems which occur with the decreasing failure rate mixed exponential distribution when the test data is censored and only a few failures are observed. For these cases sufficient conditions are obtained that...

Topics: DTIC Archive, Myhre,Janet M, CLAREMONT MEN'S COLL CA INST OF DECISION SCIENCE, *EXPERIMENTAL DATA,...

A cyclic queueing network with two servers and a finite number of customers is studied. The service times for server 1 form an EARMA(1,1) process (exponential mixed autoregressive moving average process both of order 1) which is a sequence of positively correlated exponential random variables; the process in general is not Markovian. The service times for the other server are independent with a common exponential distribution. Limiting results for the number of customers in queue and the...

Topics: DTIC Archive, Jacobs, P. A., NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *QUEUEING THEORY, *NETWORKS,...

P-values are commonly given for ordinary single stage statistical tests. In this note we give a general method for calculating p-values for a large class of multi-stage and sequential tests. We also give some tables of p-values for multi-stage tests about the parameter of an exponential distribution when test plans from MIL-STD-781C are used. (Author)

Topics: DTIC Archive, Madsen, Richard W, MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS, *STATISTICAL TESTS,...

Two integrals have been developed which are needed to solve certain problems of mathematical physics related to the Bessel and Euler equations. Integrals of this type have known application in problems using cylindrical coordinates.

Topics: NASA Technical Reports Server (NTRS), ANALYSIS (MATHEMATICS), BESSEL FUNCTIONS, COORDINATES,...

During the past few years, major emphasis in the field of Computer Economics has been given to technology-cost analysis -- in which cost was analyzed as a function of network topology, transmission technology, and reliability. Recently, the focus of research in this field seems to have changed from the 'engineering-economics' point-of-view to the rather 'pure economics' point-of-view. This report concerns itself with the purchasing behavior of those buying computing services. Software and...

Topics: DTIC Archive, Ahn, Moon-Suk, HAWAII UNIV HONOLULU, *BEHAVIOR, *COMPUTERS, *CONSUMERS, *COST...

A second order autoregressive process in exponential variables, NEAR(2), is established: the distributional assumptions involved in this model highlight is a very broad four parameter structure which combines five exponential random variables into a sixth exponential random variable. The dependency structure of the NEAR(2) process beyond and including autocorrelations is explored using some new ideas on residual analysis for non-normal processes with autoregressive correlation structure. Other...

Topics: DTIC Archive, Lewis,P A W, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *MATHEMATICAL MODELS,...

The two dimensional transient heat (diffusion) equation with Dirichlet boundary conditions was solved using the Dufort-Frankel, Saul'ev, and, Exponential (Power-law) finite fidderence schemes. All methods were investigated for oscillatory behavior and comparisons of accuracy made. To predict the time step at which oscillatory behavior would occur, the coefficient, matrix, and probabilistic methods of stability analysis were utilized. At time steps greater than the square of the mesh divided by...

Topics: DTIC Archive, Cuthrell,Joseph E, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF...

Many publications resulted from this contract, and this report contains a list of these. The publications represent the work on this contract. Keywords: Bibliographies; Normal distributions; Chi square method; Tolerance limits; T distributions; Exponential distributions.

Topics: DTIC Archive, Owen, Donald B, SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE,...

Contents: Classification and selection rules for the exponential populations; Nonparametric analysis of some reliability problems; Bayesian test for increasing failure rate; Estimation of the restricted scale parameter of the exponential distribution; Nonparametric tests for independence; Estimation of reliability in the stress-strength model; Estimates of reliability for k-out-of- m systems; Identifiability of the multinormal and other distributions under competing risks model.

Topics: DTIC Archive, Basu, Asit P, MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS, *NONPARAMETRIC STATISTICS,...

Liapunov functions of simple form have been used for the study of stability properties of difference-differential equations. In this paper, we provide necessary and sufficient conditions for the existence of such functions. (Author)

Topics: DTIC Archive, Carvalho,L A V, BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS,...

The use of importance sampling for estimation of small probabilities is illustrated by means of a signal-detection example. In particular, false alarm probabilities in the ten to the minus 7th power range are accurately estimated by means of only 1000 independent trials. The fundamental variance-reducing capability of importance sampling is explored and used to significantly improve the performance of the probability estimate for the detection example considered. Guidelines for choosing good...

Topics: DTIC Archive, Nuttall,Albert H, NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB,...

An algorithm has been developed based on the assumption that a given set of data is representable by a function that is a product of algebraic, trigonometric, and exponential polynomials. The degrees of the underlying polynomials, the optimal data spacing (optimal multiple of stepsize in tabular data), and the parameters of the approximating function are all selected by the algorithm to minimize an objective function that depends on the variance of the deviation between the data and the fitted...

Topics: DTIC Archive, Masaitis, C, ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD, *DATA REDUCTION,...

The objective of this paper is to develop acceptance procedures based on a sequential probability ratio test when the system failures follow Weibull probability distribution. The acceptance procedures in both Military Handbook 108 and Mil-Std-781C are based on exponential distribution of failures. Exponential distribution implies a constant hazard rate. The Weibull distribution is much more comprehensive and, with suitable choice of parameters, can describe constant, increasing or decreasing...

Topics: DTIC Archive, Ghare,P M, VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG, *WEIBULL DENSITY...

We present a procedure which generates all the facets of a 0-1 programming polytope P with positive coefficients in a finite number of steps. The procedure is based upon the relationship between facets of P and facets of the knapsack polytopes corresponding to certain nonnegative combinations of inequalities implied by P. Finiteness of the procedure is proven by examining the relationship of the valid inequalities generated during each step of the procedure in connection with a result due to...

Topics: DTIC Archive, Mazzola,Joseph B, CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH...

The Parabolic Equation Model is a wave acoustics model designed for the computation of acoustic transmission loss as a function of range and depth in range dependent ocean environments. The elliptic reduced wave equation is approximated by a parabolic partial differential equation that can be numerically integrated by marching the solution forward in range. The model is primarily useful for predicting low frequency ( 200 Hz) acoustic propagation of energy along waterborne paths. This report...

Topics: DTIC Archive, Brock,H K, NAVAL OCEAN RESEARCH AND DEVELOPMENT ACTIVITY NSTL STATION MS,...

For random walsk s sub n, n=1,2,... whose distribution can be imbedded in an exponential family, a method is described for determining the asymptotic behavior as m goes to infinity of P(s sub n m c(n/m) for some n m such that s sub m = m micron sub o) (micron sub 0 c(1)). Applications are given to the distribution of the Smirnov statistic and to modified repeated significance tests. (Author)

Topics: DTIC Archive, STANFORD UNIV CA DEPT OF STATISTICS, *STOCHASTIC PROCESSES, *BOUNDARIES,...

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an...

Topics: DTIC Archive, Traister,L M, INSTITUTE FOR SOFTWARE ENGINEERING PALO ALTO CA, *MATHEMATICAL MODELS,...

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Topics: Exponential functions, Logarithmic functions, Exponential functions, Logarithmic functions

In this paper some of the problems of parametric estimation for samples from distributions, which have decreasing failure rate, are discussed. Some of these distributions are obtained by mixing different exponential populations, others represent mechanisms analogous to 'work hardening' for each component where 'old is better than new'. Sufficient conditions are obtained that maximum likelihood estimators of appropriately chosen shape and scale parameters exist in both cases. The sample data...

Topics: DTIC Archive, Myhre,Janet M, CLAREMONT MEN'S COLL CA INST OF DECISION SCIENCE, *RELIABILITY,...

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, EXPONENTIAL FUNCTIONS, FOURIER SERIES,...

This paper applies the techniques of the h-p version to the boundary element method for boundary value problems on plane non-smooth domains with piecewisely analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is obtained when a geometric mesh refinement is used near the vertices. (aw)

Topics: DTIC Archive, Babuska, I, MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY,...

The effect of refractive error on the detection and identification of simple and complex targets was studied. Contrast sensitivity to sine-wave gratings of spatial frequencies from 0.61 to 22 cycles per degree with induced refractive errors of 0, +1, +2, +3, +4, +5, and +6 diopters were measured. Objective subject accommodation measurements were determined. The contrast needed to detect and identify Snellen letters and aircraft was also measured at the same levels of refractive error. In...

Topics: DTIC Archive, Cohen, Julie B., AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING,...

Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTATIONAL GRIDS, MONTE CARLO METHOD,...

An analytical and empirical model is presented for parametric study of multiple beam antenna frequency reuse capacity and interbeam isolation. Two types of reflector antennas, the axisymmetric parabolic and the offset-parabolic reflectors, are utilized to demonstrate the model. The parameters of the model are introduced and their limitations are discussed in the context of parabolic reflector antennas. The model, however, is not restricted to analysis of reflector antenna performance. Results...

Topics: NASA Technical Reports Server (NTRS), ANTENNA RADIATION PATTERNS, MATHEMATICAL MODELS, MULTIPLE...

A class of models generalizing exponential families is defined via the algebraic structure of the sufficient statistics. The maximum likelihood estimate for the unknown parameter is shown to exist and be unique. The sequence of sufficient statistics from successive repetitions of experiments corresponding to a general exponential model is shown to form an extreme family of Markov chains as defined by Lauritzen (1974).

Topics: DTIC Archive, Lauritzen, Steffen L, STANFORD UNIV CA DEPT OF STATISTICS, *STATISTICAL PROCESSES,...

One sided sequential tests for the mean of an exponential distribution are proposed, and the related confidence intervals are computed. The tests behave like the classical sequential probability ratio test when the mean is small and like a fixed time test when the mean is large and accurate estimation is important. (Author)

Topics: DTIC Archive, Siegmund,D, STANFORD UNIV CALIF DEPT OF STATISTICS, *SEQUENTIAL ANALYSIS, *CONFIDENCE...

In models of reliability growth in stages, it is usual to assume that system parameters improve monotonically from stage to stage, following some postulated law of growth. This paper explores a Bayesian model where such improvement only occurs on the average, e.g., a case when the parameters are assumed to be stochastically ordered. It is shown that the problem can be recast into a hierarchical form in which there are strictly-ordered hyperparameters which index the admissible family of ordered...

Topics: DTIC Archive, Jewell,William S, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *STOCHASTIC...

We consider infinite dimensional optimization problems involving entropy-type functionals in the objective function as well as in the constraints. A duality theory is developed for such problems and applied to the reliability rate function problem in Information Theory. Originator-supplied keywords include: Optimization in Infinite Dimensional Spaces; Dulaity in Convex Optimization; Entropy; divergence: Information Theory; Channel Capacity; Reliability Rate Function; Error Exponent Function....

Topics: DTIC Archive, Ben-Tal,A, TEXAS UNIV AT AUSTIN CENTER FOR CYBERNETIC STUDIES, *INFORMATION THEORY,...

A tractable, five-parameter family of continuous, unimodal probability distributions is developed. Special cases include the Bernoulli trial, uniform, power series, exponential, triangular and Laplace (double exponential) distributions. The family has closed-form density function, cumulative distribution function, inverse cumulative distribution function, hazard function, and residual moments. Statistical properties, parameter determination and random variate generation are discussed. Two...

Topics: DTIC Archive, Schmelser,B W, PURDUE UNIV LAFAYETTE IN SCHOOL OF INDUSTRIAL ENGINEERING,...

This paper reconsiders the classical model for selling an asset in which offers come in daily and a decision must then be made as to whether or not to sell. For each day the item remains unsold a continuation (or maintenance cost) c is incurred. The successive offers are assumed to be independent and identically distributed random variables having an unknown distribution F. The model is considered both in the case where once an offer is rejected it may not be recalled at a later time, and in...

Topics: DTIC Archive, Derman,C, STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH, *COMMERCE, *COST ANALYSIS,...

For abstract see AD-A072 984.

Topics: DTIC Archive, Whitman,G M, ARMY COMMUNICATIONS RESEARCH AND DEVELOPMENT COMMAND FORT MONMOUTH NJ,...

In this paper we apply that form of the Taylor series to the Yukawa potential, and to several potential functions which can be derived from it. In particular, we examine the expansion of the Yukawa potential itself. In the limit as the exponent a vanishes, the Yukawa potential transforms into the Coulomb potential. We show that the limiting process applied to the Taylor series for the Yukawa potential yields the familiar form of the Laplace expansion of the Coulomb potential. Differentiation of...

Topics: DTIC Archive, McKinley,J M, OAKLAND UNIV ROCHESTER MICH, *QUANTUM THEORY, *POTENTIAL THEORY,...

One major accomplishment has been the devising of a very general theory for establishing the existence of a best approximation to an arbitrary function by an exponential sum of a given order. A second result was the creation of a mathematical theory and workable numerical methods for constructing best Chebyshev, least mean, and least squares approximations for a given completely monotonic function by sums of exponentials. Finally, the compilation and publication of a bibliograph for...

Topics: DTIC Archive, Kammler ,David W, SOUTHERN ILLINOIS UNIV CARBONDALE DEPT OF MATHEMATICS, *EXPONENTIAL...

The class of time-varying linear systems which are two-time-scale on an interval may be decoupled by a time-varying transformation of variables into separate subsystems containing the slow and fast dynamic parts. The transformation is obtained by solving a nonsymmetric Riccati differential equation forward in time and a linear matrix differential equation backward in time. Small parameters are identified which measure the strength of the time scale separation and the stability of the fast...

Topics: DTIC Archive, O'Malley,Robert E , Jr, ARIZONA UNIV TUCSON DEPT OF MATHEMATICS, *LINEAR SYSTEMS,...

The adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered. In addition to the usual assumptions made regarding the plant transfer function, it is also assumed that the high frequency gain (kp) of the plant and an upper bound on the magnitude of the controller parameters, are known. Under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system.

Topics: DTIC Archive, KREISSELMEIER,Gerhard, YALE UNIV NEW HAVEN CT SYSTEMS AND INFORMATION SCIENCES,...

A finite element space-angle synthesis (FESAS) solution of the steady state anisotropic Boltzmann equation in a two-dimensional cylindrical geometry was developed. Starting from a variational principle the Bubnov-Galerkin solution method was applied to the second order even parity form of the Boltzmann equation. A trial function flux expansion in bicubic splines and spherical (surface) harmonics was used. A first scatter (collision) source and an exponentially varying atmosphere were also...

Topics: DTIC Archive, Wills,Eze E, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING,...

A comprehensive comparison of the most efficient Discrete Fourier Transform (DFT) techniques is presented. The DFT algorithms selected are the fixed radix Fast Fourier Transform (FFT), mixed radix FET, the Winograd Fourier Transform Algorithm (WFTA), and the Prime Factor Algorithm (PFA). Comparison of the algorithms is based on the number of real multiplications, additions, and memory arrays required as a function of sequence length N. This paper reviews the literature, selects the most...

Topics: DTIC Archive, Blanken,John David, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF...

A large number of reliability models have been considered under the AFOSR Grant AFOSR77-3213.

Topics: DTIC Archive, Ross,Sheldon M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *MATHEMATICAL...

This note describes how to use Brent's multiple-precision arithmetic package newly made available for the ASC. This note also enumerates some of the concomitant mathematical functions, constants and software. In addition, a comparison of computation times for the basic arithmetic operations is made between this package and the existing ASC multiple-precision arithmetic software. (Author)

Topics: DTIC Archive, Miller,A R, NAVAL RESEARCH LAB WASHINGTON DC, *COMPUTER PROGRAM DOCUMENTATION,...

In this article a systematic approach to providing goodness of fit tests is discussed, for the composite goodness of fit problem of testing that the distribution F of a random sample comes from a parametric family F sub O. Characterization procedures are emphasized, and it is shown that, at least for the exponential case, invariant characterizations appear to be better than those which are not invariant. A general technique is developed for producing invariant characterizations and for the...

Topics: DTIC Archive, O'Reilly,Federico J, STANFORD UNIV CA DEPT OF STATISTICS, *STATISTICAL TESTS,...

If the number of factors in an experiment is increased, does it necessarily follow that the size of the experiment must increase to achieve a satisfactory analysis? In some common situations the answer is No. The present paper discusses a model suggested by medical diagnostic problems in which the answer is Yes: indeed, the increase in size is exponentially fast. The conclusion is drawn that statisticians should be cautions before embarking on the study of data with large numbers of factors...

Topics: DTIC Archive, Lindley,D V, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *PARAMETRIC...